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Roth, et al - Fundamentals of Logic Design 7/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 27 / 51

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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  • Instructions

    Updated with modern coverage, a streamlined presentation, and excellent companion software, this enhanced 7th edition of Fundamentals of Logic Design, published by Cengage Learning, achieves yet again an unmatched balance between theory and application. Authors Charles H. Roth, Jr. and Larry L. Kinney, and contributing author, Eugene B. John, carefully present the theory that is necessary for understanding the fundamental concepts of logic design while not overwhelming students with the mathematics of switching theory. Divided into 20 easy-to-grasp study units, the book covers such fundamental concepts as Boolean algebra, logic gates design, flip-flops, and state machines. By combining flip-flops with networks of logic gates, students will learn to design counters, adders, sequence detectors, and simple digital systems. After covering the basics, this text presents modern design techniques using programmable logic devices and the VHDL hardware description language.

    Question 1 is a Chapter Quiz question: Encourage students to test and apply what they have learned. These questions can serve as a quick and useful self-test to help confirm understanding of each concept. Pre-built Chapter Quiz assignments have also been added to the Course Pack.

    Question 2 is an Expanded Problem exercise. An Expanded Problem addresses one or more key intermediate steps by including additional questions with answer blanks within the exercise. The goal is to give the student credit for intermediate steps as well as to nudge the student down the correct path.

    Question 3 uses circuits of switches to illustrate two theorems.

    Question 4 uses factoring to obtain a product of sums.

    Question 5 illustrates simplification of a logic gate circuit using the elimination theorem.

    Question 6 uses DeMorgan’s relationships and Involution to find the complements of some functions.

    Question 7 finds the logic function expression describing a circuit by the three methods indicated and simplifies each expression, showing that they are equal.

    Question 8 presents five Boolean algebra expressions and asks to indicate which, if any, of the following terms describe the expression: product term, sum-of-products, sum term, and product-of-sums.

    Question 9 uses a truth table to specify the output values of a specific element in a circuit in terms of the values of the input variables.

    Question 10 uses factoring to obtain a product of sums.

    Question 11 draws a circuit that uses two OR gates and two AND gates to realize a specific function.

    Questions 12 is another Expanded Problem exercise showing how the question before it, Question 11, has been expanded.

    Question 13 shows how two gate circuits realize the same function. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

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For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

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1. 1/1 points  |  Previous Answers RKFunLD7 2.CQ.001. My Notes
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1/1
 
Illustrate the following theorem using circuits of switches.
X + YZ = (X + Y)(X + Z)

Correct: Your answer is correct.
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5/5
 
For this problem, assume that inputs are available only in uncomplemented form. Do not change or simplify the given switching algebra expressions. Using AND, OR, and NOT gates construct a gate circuit that corresponds one to one with the following switching algebra expressions.
(a)
(W + Z)′

Correct: Your answer is correct.
(b)
XYZ′

Correct: Your answer is correct.
(c)
(W + Z)′ + (XYZ′)

Correct: Your answer is correct.
(d)
WX′ + Y

Correct: Your answer is correct.
(e)
(WX′ + Y) [(W + Z)′ + (XYZ′)]

Correct: Your answer is correct.
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–/1
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–/1
 
Illustrate the following theorems using circuits of switches. In each case, explain why the circuits are equivalent.
(a)
X + XY = X
(b)
X + YZ = (X + Y)(X + Z)
(Submit a file with a maximum size of 1 MB. Submissions will be graded by your instructor after the due date based on its accuracy. Your grade may change.)

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4. 1/6 points  |  Previous Answers RKFunLD7 2.7.006. My Notes
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1/6
 
Factor each of the following expressions to obtain a product of sums. (The answer to (f) should be the product of four terms, each a sum of three variables.)
(a)
AB + C'D'
(A+C′)(B+C′)(A+D′)(B+D′)
Correct: Your answer is correct. webMathematica generated answer key
(b)
WX + WY'X + ZYX
x(w+z)(w+y)
Incorrect: Your answer is incorrect. webMathematica generated answer key
(c)
A'BC + EF + DEF'
a
Incorrect: Your answer is incorrect. webMathematica generated answer key
(d)
XYZ + W'Z + XQ'Z
x
Incorrect: Your answer is incorrect. webMathematica generated answer key
(e)
ACD' + C'D' + A'C
z
Incorrect: Your answer is incorrect. webMathematica generated answer key
(f)
A + BC + DE
b
Incorrect: Your answer is incorrect. webMathematica generated answer key
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5. –/2 points RKFunLD7 2.6.009. My Notes
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–/2
 
Find F and G and simplify.
Two figures depict logic circuits. Refer to the adjacent tabs for more details.
A logic circuit with 6 gates and 2 inputs. The circuit will be read from the final output to the inputs.
  1. The final AND gate has output F and two inputs.
    1. The first input to the final AND gate is the output from an OR gate.
    2. The second input to the final AND gate is the output from a NOT gate.
      1. The OR gate has two inputs.
        1. The first input to the OR gate is the output from a NOT gate.
          1. The NOT gate has one input.
            1. The input to the NOT gate is an OR gate.
              1. The OR gate has two inputs.
                1. The first input to the OR gate is A.
                2. The second input to the OR gate is B.
        2. The second input to the OR gate is the output from the NOT gate that is also an input to the final AND gate.
          1. The NOT gate has one input.
            1. The input to the NOT gate is an OR gate.
              1. The first input to the OR gate is the NOT gate that is the first NOT gate that is an input to the OR gate that is an input to the final AND gate.
              2. The second input to the OR gate is A.
A logic circuit with 9 gates and 4 inputs. The circuit will be read from the final output to the inputs.
  1. The final NOT gate has output G and one input.
    1. The first input to the final NOT gate is the output from an AND gate.
      1. The AND gate has two inputs.
        1. The first input to the AND gate is the output from a NOT gate.
          1. The NOT gate has one input.
            1. The first input to the NOT gate is the output from an AND gate.
              1. The AND gate has three inputs.
                1. The first input to the AND gate is the output from a NOT gate.
                  1. The NOT gate has one input.
                    1. The first input to the NOT gate is the output from an OR gate.
                      1. The OR gate has three inputs.
                        1. The first input to the OR gate is R.
                        2. The second input to the OR gate is S.
                        3. The third input to the OR gate is T.
                2. The second input to the AND gate is P.
                3. The third input to the AND gate is the output from an AND gate.
                  1. The AND gate has two inputs.
                    1. The first input to the AND gate is the output from a NOT gate.
                      1. The NOT gate has one input.
                        1. The first input to the NOT gate is the output from an OR gate.
                          1. The OR gate has two inputs.
                            1. The first input to the OR gate is R.
                            2. The second input to the OR gate is S.
                    2. The second input to the AND gate is T.
        2. The second input to the AND gate is T.
F =
(A+B)′
G =
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1/2
 
Use only DeMorgan's relationships and Involution to find the complements of the following functions.
(a)
f(A, B, C, D) = [A + (BCD)'] [(AD)' + B(C' + A)]
f '(A, B, C, D) =
A′BCD + AD(B′ + CA′)
Correct: Your answer is correct. webMathematica generated answer key
(b)
f(A, B, C, D) = AB'C + (A'+ B + D)(ABD'+ B')
f '(A, B, C, D) =
(A′+B+C′)
Incorrect: Your answer is incorrect. webMathematica generated answer key
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–/2
 
For the switching circuit below, find the logic function expression F describing the circuit by the three methods indicated, simplify each expression, and show that they are equal.
A circuit consists of six open switches. Starting from a left terminal, a wire goes to the right and splits into two parallel branches.
  • The upper branch splits into two parallel sub-branches, where the upper sub-branch contains open switch A' and the lower sub-branch contains open switch B'. The sub-branches recombine. The upper branch continues right to reach open switch C, then continues right to recombine with the lower branch.
  • The lower branch contains open switch A, then splits into two parallel sub-branches. The upper sub-branch contains open switch B and the lower sub-branch contains open switch C '. The sub-branches recombine. The lower branch continues right to recombine with the upper branch and end at a right terminal.
(a)
subdividing it into series and parallel connections of subcircuits until single switches are obtained
(b)
finding all paths through the circuit (sometimes called tie sets), forming an AND term for each path and ORing the AND terms together
(c)
finding all ways of breaking all paths through the circuit (sometimes called cut sets), forming an OR term for each cut set and ANDing the OR terms together
(Submit a file with a maximum size of 1 MB. Submissions will be graded by your instructor after the due date based on its accuracy. Your grade may change.)

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Enter the simplified expression. (Use the following as necessary: A, B, and C.)
F =
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8. 3/5 points  |  Previous Answers RKFunLD7 2.6.018. My Notes
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3/5
 
For each of the following Boolean (or switching) algebra expressions, indicate which, if any, of the following terms describe the expression: product term, sum-of-products, sum term, and product-of-sums. (Select all that apply.)
(a)
H'D
Incorrect: Your answer is incorrect.

(b)
HD' + DF
Correct: Your answer is correct.

(c)
(H' + D)(BH + F)
Correct: Your answer is correct.

(d)
H + F
Incorrect: Your answer is incorrect.

(e)
(H' + D)(B + F)(H + D' + F')
Correct: Your answer is correct.

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9. 16/16 points  |  Previous Answers RKFunLD7 2.3.021. My Notes
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1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1
1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100
Total
16/16
 
In the following circuit,
F = (A' + B)C.
A logic circuit with 3 gates and 3 inputs. The circuit will be read from the final output to the inputs.
  1. The final OR gate has output H and two inputs.
    1. The first input to the final OR gate is the output, F, from an unspecified gate.
      1. The unspecified gate has three inputs.
        1. The first input to the unspecified gate is A.
        2. The second input to the unspecified gate is B.
        3. The third input to the unspecified gate is C.
    2. The second input to the final OR gate is the output, G, from an unspecified gate.
      1. The unspecified gate has the same three inputs.
        1. The first input to the unspecified gate is A.
        2. The second input to the unspecified gate is B.
        3. The third input to the unspecified gate is C.
Give a truth table for F and G so that H is as specified in its truth table. If G can be either 0 or 1 for some input combination, leave its value unspecified by selecting "x".
A B C H F G
0 0 0 0 Correct: Your answer is correct. seenKey

0

 		Correct: Your answer is correct. seenKey

0
0 0 1 1 Correct: Your answer is correct. seenKey

1

 		Correct: Your answer is correct. seenKey

x
0 1 0 1 Correct: Your answer is correct. seenKey

0

 		Correct: Your answer is correct. seenKey

1
0 1 1 1 Correct: Your answer is correct. seenKey

1

 		Correct: Your answer is correct. seenKey

x
1 0 0 0 Correct: Your answer is correct. seenKey

0

 		Correct: Your answer is correct. seenKey

0
1 0 1 1 Correct: Your answer is correct. seenKey

0

 		Correct: Your answer is correct. seenKey

1
1 1 0 0 Correct: Your answer is correct. seenKey

0

 		Correct: Your answer is correct. seenKey

0
1 1 1 1 Correct: Your answer is correct. seenKey

1

 		Correct: Your answer is correct. seenKey

x
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10. –/4 points RKFunLD7 2.7.023. My Notes
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–/4
 
Factor each of the following expressions to obtain a product of sums.
(a)
W + U'YV
(W+U′)(W+Y)((W+V))
(b)
TW + UY' + V
(c)
A'B'C + B'CD' + B'E'
(d)
ABC + ADE' + ABF'
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11. 0/1 points  |  Previous Answers RKFunLD7 2.6.027. My Notes
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1/100
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0/1
 
Draw a circuit that uses two OR gates and one AND gate to realize the following function.
F = (V + X + Y)(V + Z)

Incorrect: Your answer is incorrect.
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–/4
 
(a)
Simplify the expression.
(X + Y)(X + Z)
(b)
Simplify the expression.
(V + X + W)(V + X + Y)
(c)
Simplify the function using the Distributive Law.
F = (V + W + X)(V + X + Y)(V + Z)
(d)
Draw a circuit that uses two or gates and two and gates only to realize the following function. (Use the simplified expression to the draw the circuit.)
F = (V + W + X)(V + X + Y)(V + Z)

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Show that the following two gate circuits realize the same function. (Submit a file with a maximum size of 1 MB. Submissions will be graded by your instructor after the due date based on its accuracy. Your grade may change.)
(a)
A logic circuit has 7 gates and 3 inputs. The circuit will be read from the final output to the inputs.
  1. The final or gate has output F and two inputs.
    1. The first input to the final or gate is the output from an and gate.
      1. The and gate has two inputs.
        1. The first input to the and gate is the output from an or gate.
          1. The or gate has two inputs.
            1. The first input to the or gate is X.
            2. The second input to the or gate is the output from a not gate.
              1. The not gate has one input.
                1. The input to the not gate is Y.
        2. The second input to the and gate is Z.
    2. The second input to the final or gate is the output from an and gate.
      1. The and gate has three inputs.
        1. The first input to the and gate is the output from a not gate.
          1. The not gate has one input.
            1. The input to the not gate is X.
        2. The second input to the and gate is Y.
        3. The third input to the and gate is the output from a not gate.
          1. The not gate has one input.
            1. The input to the not gate is Z.
(b)
A logic circuit has 7 gates and 3 inputs. The circuit will be read from the final output to the inputs.
  1. The final and gate has output G and three inputs.
    1. The first input to the final and gate is the output from an or gate.
      1. The or gate has three inputs.
        1. The first input to the or gate is X.
        2. The second input to the or gate is the output from a not gate.
          1. The not gate has one input.
            1. The input to the not gate is Y.
        3. The third input to the or gate is the output from a not gate.
          1. The not gate has one input.
            1. The input to the not gate is Z.
    2. The second input to the final and gate is the output from an or gate.
      1. The or gate has two inputs.
        1. The first input to the or gate is the output from a not gate.
          1. The not gate has one input.
            1. The input to the not gate is X.
        2. The second input to the or gate is Z.
    3. The third input to the final and gate is the output from an or gate.
      1. The or gate has two inputs.
        1. The first input to the or gate is Z.
        2. The second input to the or gate is Y.

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What is the function? (Use the following as necessary: X, Y, and Z.)
F = G =
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